Multi-scale Feature Learning Dynamics: Insights for Double Descent

• URL: http://arxiv.org/abs/2112.03215v1
• Date: Mon, 6 Dec 2021 18:17:08 GMT
• Title: Multi-scale Feature Learning Dynamics: Insights for Double Descent
• Authors: Mohammad Pezeshki, Amartya Mitra, Yoshua Bengio, Guillaume Lajoie
• Abstract summary: We study the phenomenon of "double descent" of the generalization error. We find that double descent can be attributed to distinct features being learned at different scales.
• Score: 71.91871020059857
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial dynamics lead to intriguing behaviors such as the phenomenon of "double descent" of the generalization error. The more commonly studied aspect of this phenomenon corresponds to model-wise double descent where the test error exhibits a second descent with increasing model complexity, beyond the classical U-shaped error curve. In this work, we investigate the origins of the less studied epoch-wise double descent in which the test error undergoes two non-monotonous transitions, or descents as the training time increases. By leveraging tools from statistical physics, we study a linear teacher-student setup exhibiting epoch-wise double descent similar to that in deep neural networks. In this setting, we derive closed-form analytical expressions for the evolution of generalization error over training. We find that double descent can be attributed to distinct features being learned at different scales: as fast-learning features overfit, slower-learning features start to fit, resulting in a second descent in test error. We validate our findings through numerical experiments where our theory accurately predicts empirical findings and remains consistent with observations in deep neural networks.

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